Infinity!?!Key academics1 (scholars and scientists) would like to retire the concept of infinity. It is too controversial. Religions of every flavor controlled it for thousands of years. Isaac Newton foiled their iron grip with his concept of absolute space and time. And even more recently, scholars developed a “work around” called renormalization for a very small part of physics. Other disciplines just assumed they’d figure out their own work around. They haven’t. Nobody has.

Nobody has gotten “beyond infinity.”

Even today, our best religious leaders and thinkers are just not compelling enough. In the face of our scientific cultures, their stories and heroes seem more like fables, wishful thinking, fiction, and fantasy. As a group, they are even fair game for the shock jock or shock talk people.

Infinity is increasingly maligned. Going from one iron grip to another, Isaac’s went limp when he looked into Einstein’s mirror. Too complex for most of us — even the best of our physicists — nothing survives scientific scrutiny and simple logic so we hop from fad-to-fad when we should be asking more questions and different kinds of questions:

• Is there such a thing as perfection within this quantum-chaotic universe? How can we capture the essence of our most perfect moments without becoming solipsistic?

• What could be infinite without becoming emotional, divisive, or even repugnant?

In 1959 I began asking myself questions about absolutes — I didn’t like what I was learning in Sunday School. By 1969, as a new college graduate, I asked myself, “How do we describe a perfect moment? Can there be any perfection within a quantum world and universe?” I arrived at three concepts; though abstract, each built on the next and had logical, mathematical and scientific meaning: continuity, symmetry, and harmony. It seemed that continuity was most basic. From it we get numbers and a sense of order. We observe symmetries everywhere. With symmetry we get geometries and a way to define simple relations. Then, I thought, “Let’s get real. Real is complex.” I liked the concept of harmony. Within music, it is real and can be exquisitely complex. Then, there were those special feelings one gets within our young love, so harmony it is. The third face of an infinite moment! With harmony we get dynamics. There’s a convergence of symmetries; some symmetries work together, others do not. And, throughout the ages, there are people like Johannes Kepler who feel a deep and ancient harmony of the spheres.

I made a study of it, but it wasn’t until I discovered how small our universe truly is that the concept, an access path to the infinite, took on special importance:• What are dimensionless constants? What is pi? What is light?• What is Planck charge? How does it manifest? What is its relation to light? …to mass? …to the key dimensionless constants?

Those questions emerged late in 2011 in a high school geometry class where I had been helping out. That day I learned something new: “There are 202 base-2 notations from the Planck base units to the current time and size of the universe.” It was, and still is, such a startling fact, it has slowly changed my life.

The finite is very finite. Take any object you can easily hold in the palm of your hand. Divide it in half. Then divide that in half. Keep going. Of course, it’ll get so small, you can only do this on paper or in your imagination. But did you know that within just 45 divisions by two, you will be smaller than an atom. You’ll be looking at protons, electrons, and neutrons (fermions) inside the atom.

But, we won’t stop there. Let’s keep dividing by two. In 67 additional steps, you will be facing what we call the Planck Wall.2 Your units of space and time will have “maxed out” because you can’t go any further. You cannot get any smaller. In summary, you can divide anything you can hold in your hand by two, 112 times and then you can’t go any smaller. Fascinating, isn’t it?

The next part just staggers the imagination. I couldn’t believe it. Please return to that object in your hand and multiply it by two. Then again and again and again. In just 90 steps, that object will become the size of the universe today. You are reading that correctly; it takes just 90 additional doublings. In a total of 202 steps, all simple doublings, you have a highly-ordered universe from the smallest possible object (a thing) to the largest. Did you know that? I didn’t until we just happened to back into the fact while fooling around with numbers and objects in that high school geometry class.

Is logic always logical? Are mathematical systems always logical? Over the years, I have written dozens of postings to explore this data. It is not trivial. It is logical, geometrical, and mathematical. If it doesn’t work, we’ve got some serious problems. Today, I am deep-into-the process of learning more. It has taken me awhile. Life has a way of interrupting one’s study. Plus, changing one’s orientation to life is not easy. New concepts take time to digest and then integrate within our system.

I was glad to be introduced to Buzz Lightyear in November 2018. Singlehandedly, Buzz, with his high-sounding mission — “To infinity and beyond” — and overall popularity, has pulled infinity back out on center stage. It is an opportunity for all of us to re-engage the inner workings of infinity. I would especially encourage thoughtful reflections about those three words — continuity, symmetry and harmony — as a way to begin to re-engage infinity in new light.

Getting beyond Buzz Lightyear’s “beyond…” If I were to guide a person into this maze of new ideas and concepts, I would first begin with the numbers, then consider the doubling mechanisms. And then, we all need to engage the mathematics, going from the most simple to the most complex. That’s just a start. We’ll need to open up our understanding of infinity and only then, perhaps we will begin to understand ourselves, our universe, and our reason for being.

To that end, I have outlined and linked some of the work done over the years to begin to grasp the meaning of it all.

Euler. The universe is fundamentally exponential. Euler’s identity is universal.

In process: Each notation will be analyzed, notation by notation. It will be within this format this unified theory could possibly unfold. Wouldn’t the role of prime numbers be to determine when new mathematical systems can be introduced?

4. Infinity. Given light’s pervasiveness, three aspects of light are taken as qualities that appear to be shared with the infinite. These are:

Continuity. Order / numbers, first within the dimensionless constants, never-ending, never repeating, and then with the progression of spheres.

Symmetry. Relations / Geometries, first with the symmetry of the spheres, then the symmetry within the tetrahedrons and octahedrons that are generated.

Harmony. Dynamics / Space-time where two symmetries actively interact as a moment of space-time; it is a qualitative moment we experience as harmony.

[2] Planck Wall: As of January 2019, there are 5400 references using Google Search to the words, “Planck Wall” (delimited by use of the quotes). Most of them refer to big bang cosmology. The limitations of big bang cosmology are well known. See: https://81018.com/2016/10/13/flood/ Although an initial survey of those 5400 references did not find any that addressed the finite-infinite relation, much more study will be done of each. Within this model the Planck Wall is quite porous, punctured with no less than 31 dimensionless constants. These are the initial bridges between the finite and infinite and make up what could be called a transformation nexus.

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More References, Resources, and Research

The Principia

Though part of the intellectual debates about boundaries, going back 3000 years and more, our particular brand of it comes from Sir Isaac Newton, a point of view formalized in his 1687 book, generally known as The Principia.

If you look up into the heavens on a clear, crisp evening, it looks like it goes on forever. That’s Newton. Another person might say, “It goes just as far as the current expansion of the universe.” To which one of the kids quickly ask, “Well, what’s behind that?” To which I would reply, “infinity.” And, of course, that begs the question, “What’s infinity?”

Infinity is not an easy concept to grasp. As a recent college graduate in 1969, I remember asking myself, “How can we take religion out of infinity and make it more accessible to everyone?” The effort by scholars has become a formal discipline called renormalization. And like so much of scholarship, it is not easy for regular people to understand. Even scholars have problems with it. Freeman Dyson worked on it back in 1949 and more recently, Steven Weinberg re-formalized it in 1986. Infinity is such a character, it needs to be corralled so the work of mathematicians and physicists can go on. Of course, it can’t be corralled, but it can appear to be tamed enough to carry on one’s work without getting bitten too badly.